RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-08_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.66 24.3585 0.889984 2 to 25 15.60 12.1442 0.208672 3 to 26 15.49 37.1921 0.996831 4 to 27 15.69 18.8272 0.661460 5 to 28 15.62 14.1262 0.341850 6 to 29 15.79 20.0301 0.727309 7 to 30 15.89 28.2314 0.957694 8 to 31 15.65 20.3003 0.740843 9 to 32 15.77 19.2460 0.685402 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.057778 Tough bday spacings test for dh-ranFile-2015-11-08_10:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 7 42 75 105 88 79 63 24 9 4 4 (O-E)^2/E 0.5 0.8 0.0 0.5 1.0 0.0 2.3 1.1 2.3 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 9.616, p= 0.525 RESULTS OF GCD FOR dh-ranFile-2015-11-08_10:31 Euclid's algorithm: p-value, steps to gcd: 0.761102 p-value, dist. of gcd's: 0.150039 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-08_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.547 0.994 0.929 0.436 0.388 0.525 0.280 0.950 Bits 8 to 15---> 0.043 0.181 0.515 0.457 0.610 0.981 0.888 0.660 Bits 16 to 23---> 0.631 0.276 0.450 0.417 0.169 0.315 0.144 0.432 Bits 24 to 31---> 0.668 0.992 0.856 0.110 0.759 0.675 0.417 0.950 KS test for the above 32 p values: 0.714 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-08_10:31, p-values for 5 runs: 0.5900, 0.5105, 0.6925, 0.8190, 0.6955 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-08_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 189 211.4 2.377 2.377 r= 29 5194 5134.0 0.701 3.078 r= 30 23135 23103.0 0.044 3.122 r= 31 11482 11551.5 0.418 3.541 chi-square = 3.541 with df = 3; p-value = 0.684 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-08_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5087 5134.0 0.430 0.491 r= 31 23123 23103.0 0.017 0.508 r= 32 11575 11551.5 0.048 0.556 chi-square = 0.556 with df = 3; p-value = 0.094 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-08_10:31 b-rank test for bits 1 to 8, p=0.12368 b-rank test for bits 2 to 9, p=0.21995 b-rank test for bits 3 to 10, p=0.78419 b-rank test for bits 4 to 11, p=0.61740 b-rank test for bits 5 to 12, p=0.52486 b-rank test for bits 6 to 13, p=0.42149 b-rank test for bits 7 to 14, p=0.33144 b-rank test for bits 8 to 15, p=0.41408 b-rank test for bits 9 to 16, p=0.03220 b-rank test for bits 10 to 17, p=0.12949 b-rank test for bits 11 to 18, p=0.49910 b-rank test for bits 12 to 19, p=0.57409 b-rank test for bits 13 to 20, p=0.48204 b-rank test for bits 14 to 21, p=0.73520 b-rank test for bits 15 to 22, p=0.36650 b-rank test for bits 16 to 23, p=0.14125 b-rank test for bits 17 to 24, p=0.06445 b-rank test for bits 18 to 25, p=0.47094 b-rank test for bits 19 to 26, p=0.24095 b-rank test for bits 20 to 27, p=0.59089 b-rank test for bits 21 to 28, p=0.83526 b-rank test for bits 22 to 29, p=0.51595 b-rank test for bits 23 to 30, p=0.50527 b-rank test for bits 24 to 31, p=0.93027 b-rank test for bits 25 to 32, p=0.98633 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.623024 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-08_10:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 141806 -0.24 0.404613 2 141460 -1.05 0.146897 3 141336 -1.34 0.090195 4 141504 -0.95 0.171811 5 141111 -1.87 0.031073 6 141908 -0.00 0.498760 7 142140 0.54 0.705039 8 141903 -0.01 0.494100 9 141308 -1.40 0.080014 10 141968 0.14 0.554516 11 141848 -0.14 0.443029 12 142318 0.95 0.830170 13 142311 0.94 0.826001 14 141997 0.20 0.581150 15 142080 0.40 0.654966 16 141913 0.01 0.503421 17 141842 -0.16 0.437499 18 141938 0.07 0.526704 19 141753 -0.37 0.357460 20 141636 -0.64 0.261535 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-08_10:31 Bits used No. missing words z-score p-value 23 to 32 141981 0.2471 0.597599 22 to 31 141669 -0.8287 0.203630 21 to 30 141556 -1.2184 0.111540 20 to 29 141978 0.2368 0.593591 19 to 28 141842 -0.2322 0.408202 18 to 27 141654 -0.8804 0.189308 17 to 26 141883 -0.0908 0.463829 16 to 25 141420 -1.6873 0.045769 15 to 24 142313 1.3920 0.918034 14 to 23 142253 1.1851 0.882005 13 to 22 141675 -0.8080 0.209535 12 to 21 141690 -0.7563 0.224732 11 to 20 142123 0.7368 0.769376 10 to 19 142297 1.3368 0.909355 9 to 18 141812 -0.3356 0.368579 8 to 17 141545 -1.2563 0.104502 7 to 16 141665 -0.8425 0.199749 6 to 15 141607 -1.0425 0.148586 5 to 14 141445 -1.6011 0.054673 4 to 13 141766 -0.4942 0.310568 3 to 12 141990 0.2782 0.609560 2 to 11 141949 0.1368 0.554403 1 to 10 141945 0.1230 0.548947 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-08_10:31 Bits used No. missing words z-score p-value 28 to 32 142140 0.7819 0.782873 27 to 31 142107 0.6701 0.748593 26 to 30 141953 0.1480 0.558842 25 to 29 142154 0.8294 0.796558 24 to 28 142297 1.3141 0.905600 23 to 27 142202 0.9921 0.839426 22 to 26 141725 -0.6248 0.266036 21 to 25 141924 0.0497 0.519831 20 to 24 141466 -1.5028 0.066444 19 to 23 141364 -1.8486 0.032260 18 to 22 141906 -0.0113 0.495497 17 to 21 141686 -0.7571 0.224510 16 to 20 141910 0.0023 0.500906 15 to 19 141598 -1.0554 0.145631 14 to 18 141632 -0.9401 0.173583 13 to 17 141386 -1.7740 0.038032 12 to 16 141860 -0.1672 0.433598 11 to 15 142033 0.4192 0.662473 10 to 14 142176 0.9040 0.816993 9 to 13 141759 -0.5096 0.305168 8 to 12 142369 1.5582 0.940407 7 to 11 141897 -0.0418 0.483330 6 to 10 141863 -0.1571 0.437602 5 to 9 142227 1.0768 0.859226 4 to 8 141551 -1.2147 0.112244 3 to 7 141952 0.1446 0.557504 2 to 6 141904 -0.0181 0.492792 1 to 5 141648 -0.8859 0.187845 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-08_10:31 Bits used No. missing words z-score p-value 31 to 32 141874 -0.1042 0.458498 30 to 31 141646 -0.7768 0.218643 29 to 30 141622 -0.8476 0.198336 28 to 29 141835 -0.2193 0.413223 27 to 28 142089 0.5300 0.701944 26 to 27 141800 -0.3225 0.373534 25 to 26 142257 1.0256 0.847454 24 to 25 141557 -1.0393 0.149328 23 to 24 142150 0.7099 0.761130 22 to 23 141715 -0.5732 0.283240 21 to 22 141759 -0.4435 0.328720 20 to 21 142084 0.5153 0.696811 19 to 20 142095 0.5477 0.708051 18 to 19 141996 0.2557 0.600895 17 to 18 141963 0.1583 0.562897 16 to 17 142357 1.3206 0.906676 15 to 16 142282 1.0993 0.864186 14 to 15 142105 0.5772 0.718097 13 to 14 142051 0.4179 0.661992 12 to 13 142145 0.6952 0.756532 11 to 12 141841 -0.2016 0.420129 10 to 11 141916 0.0197 0.507849 9 to 10 142273 1.0728 0.858314 8 to 9 141233 -1.9951 0.023017 7 to 8 141553 -1.0511 0.146602 6 to 7 141854 -0.1632 0.435174 5 to 6 142142 0.6863 0.753751 4 to 5 141802 -0.3166 0.375771 3 to 4 142107 0.5831 0.720086 2 to 3 141912 0.0079 0.503142 1 to 2 141825 -0.2488 0.401773 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-08_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2544.23 0.626 0.734183 Test results for specific bytes for dh-ranFile-2015-11-08_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2606.44 1.505 0.933873 2 to 9 2403.58 -1.364 0.086355 3 to 10 2561.76 0.873 0.808800 4 to 11 2635.92 1.922 0.972714 5 to 12 2512.21 0.173 0.568570 6 to 13 2511.36 0.161 0.563839 7 to 14 2613.81 1.610 0.946249 8 to 15 2432.21 -0.959 0.168849 9 to 16 2567.10 0.949 0.828664 10 to 17 2526.49 0.375 0.646056 11 to 18 2390.14 -1.554 0.060128 12 to 19 2471.09 -0.409 0.341326 13 to 20 2439.23 -0.859 0.195036 14 to 21 2584.87 1.200 0.884967 15 to 22 2471.02 -0.410 0.340977 16 to 23 2564.37 0.910 0.818677 17 to 24 2527.54 0.389 0.651543 18 to 25 2550.34 0.712 0.761747 19 to 26 2477.10 -0.324 0.373037 20 to 27 2440.60 -0.840 0.200430 21 to 28 2551.58 0.729 0.767127 22 to 29 2457.40 -0.602 0.273454 23 to 30 2609.07 1.543 0.938527 24 to 31 2559.34 0.839 0.799317 25 to 32 2423.34 -1.084 0.139158 CDPARK for dh-ranFile-2015-11-08_10:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3543 0.9132 0.819442 3569 2.1005 0.982156 3538 0.6849 0.753306 3508 -0.6849 0.246694 3477 -2.1005 0.017844 3518 -0.2283 0.409702 3495 -1.2785 0.100530 3533 0.4566 0.676028 3525 0.0913 0.536383 3538 0.6849 0.753306 Square side=100, avg. no. parked=3524.40 sample std.=24.90 p-value of the KSTEST for those 10 p-values: 0.893183 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-08_10:31 0.5918,0.8610,0.3055,0.9147,0.5419,0.1938,0.9059,0.2047,0.5880,0.6461, The KS test for those 10 p-values: 0.595405 The 3DSPHERES test for dh-ranFile-2015-11-08_10:31 sample no r^3 equiv. uni. 1 27.370 0.598420 2 19.335 0.475080 3 72.185 0.909840 4 21.088 0.504861 5 22.926 0.534296 6 17.430 0.440665 7 51.191 0.818479 8 24.790 0.562352 9 11.126 0.309874 10 25.786 0.576643 11 23.555 0.543964 12 18.330 0.457195 13 22.050 0.520493 14 8.892 0.256509 15 33.258 0.669984 16 69.931 0.902805 17 17.994 0.451078 18 7.348 0.217248 19 1.909 0.061651 20 8.109 0.236841 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.289938 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-08_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.4 -0.1 0.4 0.3 -0.5 -0.9 -0.8 -0.6 -0.7 -0.3 -0.7 -1.0 0.3 0.9 -0.1 -0.3 0.1 1.0 0.8 0.7 3.2 -0.4 -0.3 -1.0 -2.3 -1.4 2.2 -1.3 -0.2 -0.3 -0.8 0.3 1.2 0.2 -0.5 0.8 -1.2 1.0 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:39.824353 z-score=-0.237383, p-value=0.433106 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-08_10:31 Test no p-value 1 0.070513 2 0.003271 3 0.576136 4 0.567102 5 0.445025 6 0.118438 7 0.833037 8 0.117025 9 0.062181 10 0.405102 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.044174 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-08_10:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66549 0.21 66859 0.55 3 25000.00 24971 0.03 24871 0.67 4 6666.67 6777 1.83 6581 1.10 5 1388.89 1415 0.49 1408 0.26 6 238.10 239 0.00 226 0.61 7 34.72 41 1.14 47 4.34 8 4.96 7 0.84 7 0.84 p=0.39552 p=0.78851 Number of rngs required: 689387, p-value: 0.873 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-08_10:31 No. of wins: Observed Expected 98361 98585.9 z-score=-1.006, pvalue=0.15728 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66393 66666.7 1.123 1.123 2 37644 37654.3 0.003 1.126 3 27076 26954.7 0.546 1.672 4 19284 19313.5 0.045 1.717 5 13825 13851.4 0.050 1.767 6 9841 9943.5 1.057 2.825 7 7349 7145.0 5.823 8.648 8 5161 5139.1 0.094 8.741 9 3651 3699.9 0.645 9.387 10 2768 2666.3 3.879 13.266 11 1897 1923.3 0.360 13.626 12 1451 1388.7 2.791 16.418 13 1020 1003.7 0.264 16.682 14 754 726.1 1.069 17.751 15 529 525.8 0.019 17.770 16 365 381.2 0.684 18.454 17 278 276.5 0.008 18.462 18 192 200.8 0.388 18.850 19 155 146.0 0.557 19.407 20 104 106.2 0.046 19.453 21 263 287.1 2.025 21.478 Chisq= 21.48 for 20 degrees of freedom, p= 0.63052 SUMMARY of craptest p-value for no. of wins: 0.157280 p-value for throws/game: 0.630517 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-08_10:31 No. of wins: Observed Expected 98808 98585.9 z-score= 0.994, pvalue=0.83978 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66590 66666.7 0.088 0.088 2 37735 37654.3 0.173 0.261 3 26961 26954.7 0.001 0.262 4 19192 19313.5 0.764 1.026 5 13892 13851.4 0.119 1.145 6 9898 9943.5 0.209 1.354 7 7228 7145.0 0.964 2.317 8 5065 5139.1 1.068 3.385 9 3739 3699.9 0.414 3.799 10 2712 2666.3 0.783 4.582 11 1923 1923.3 0.000 4.582 12 1377 1388.7 0.099 4.682 13 1018 1003.7 0.203 4.885 14 738 726.1 0.194 5.079 15 516 525.8 0.184 5.263 16 400 381.2 0.932 6.195 17 307 276.5 3.355 9.550 18 188 200.8 0.820 10.370 19 142 146.0 0.109 10.478 20 109 106.2 0.073 10.551 21 270 287.1 1.020 11.572 Chisq= 11.57 for 20 degrees of freedom, p= 0.06997 SUMMARY of craptest p-value for no. of wins: 0.839778 p-value for throws/game: 0.069966 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0033,0.0178,0.0230,0.0311,0.0322,0.0323,0.0380,0.0433,0.0442,0.0458, 0.0547,0.0578,0.0601,0.0617,0.0622,0.0644,0.0664,0.0700,0.0705,0.0800, 0.0864,0.0902,0.0936,0.1005,0.1045,0.1097,0.1115,0.1122,0.1170,0.1184, 0.1237,0.1295,0.1392,0.1412,0.1436,0.1456,0.1466,0.1469,0.1486,0.1493, 0.1500,0.1573,0.1687,0.1688,0.1718,0.1736,0.1808,0.1878,0.1893,0.1938, 0.1950,0.1983,0.1997,0.2004,0.2036,0.2047,0.2087,0.2095,0.2172,0.2186, 0.2200,0.2245,0.2247,0.2368,0.2410,0.2467,0.2565,0.2615,0.2660,0.2735, 0.2762,0.2801,0.2832,0.2899,0.3052,0.3055,0.3099,0.3106,0.3147,0.3287, 0.3314,0.3410,0.3413,0.3418,0.3575,0.3665,0.3686,0.3730,0.3735,0.3758, 0.3884,0.3955,0.4018,0.4046,0.4051,0.4082,0.4097,0.4132,0.4141,0.4165, 0.4174,0.4201,0.4215,0.4325,0.4331,0.4336,0.4352,0.4356,0.4375,0.4376, 0.4407,0.4430,0.4450,0.4498,0.4511,0.4572,0.4573,0.4585,0.4638,0.4709, 0.4751,0.4820,0.4833,0.4928,0.4941,0.4955,0.4988,0.4991,0.5009,0.5031, 0.5034,0.5049,0.5053,0.5078,0.5105,0.5149,0.5159,0.5198,0.5205,0.5249, 0.5252,0.5254,0.5267,0.5343,0.5364,0.5419,0.5440,0.5466,0.5489,0.5544, 0.5545,0.5575,0.5588,0.5624,0.5629,0.5638,0.5671,0.5686,0.5741,0.5761, 0.5766,0.5812,0.5880,0.5900,0.5909,0.5918,0.5936,0.5954,0.5976,0.5984, 0.6009,0.6096,0.6104,0.6174,0.6230,0.6305,0.6307,0.6461,0.6461,0.6515, 0.6550,0.6596,0.6615,0.6620,0.6625,0.6675,0.6700,0.6752,0.6760,0.6845, 0.6854,0.6925,0.6955,0.6968,0.7019,0.7050,0.7081,0.7139,0.7181,0.7201, 0.7273,0.7342,0.7352,0.7408,0.7486,0.7533,0.7533,0.7538,0.7565,0.7594, 0.7611,0.7611,0.7617,0.7671,0.7694,0.7829,0.7842,0.7885,0.7966,0.7993, 0.8088,0.8170,0.8185,0.8187,0.8190,0.8194,0.8260,0.8287,0.8302,0.8330, 0.8353,0.8394,0.8398,0.8475,0.8557,0.8583,0.8592,0.8610,0.8642,0.8734, 0.8820,0.8850,0.8879,0.8900,0.8932,0.9028,0.9056,0.9059,0.9067,0.9094, 0.9098,0.9147,0.9180,0.9290,0.9303,0.9339,0.9385,0.9404,0.9462,0.9500, 0.9502,0.9577,0.9727,0.9812,0.9822,0.9863,0.9920,0.9938,0.9968, Overall p-value after applying KStest on 269 p-values = 0.510634 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.